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It means that the complex valued modulation symbols obtained as a result of the modulation scheme block (QPSK< 16-QAM, or 64-QAM) are mapped to resource elements in the 2D time-frequency resource grid. Suppose that the UE is assigned 1 resource block for transmission. That is 12 resource elements that can be used during one OFDMA symbol duration. Hope this helps.
The x-axis in the second diagram refers to time (in the unit of OFDM symbols), and the y-axis is the subcarrier index. If a user is assigned a set of squares in the second diagram, it means that that user can transmit on those subcarriers in that symbol. As an example, let user 1 be assigned to subcarriers 15-25 in symbol 1, and then silent after that. This means that in the first OFDM symbol, the subcarriers 15-25 would contain data from user 1, and afterwards would be reallocated for some other purpose for successive symbols.